How do you simplify the expression $sin^4theta-cos^4theta$ ?

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Answer 1 · 2018-05-15T07:19:45

$sin^4theta-cos^4theta=-cos2theta$

$sin^4theta-cos^4theta$

= $(sin^2theta)^2-(cos^2theta)^2$
(and using $(a^2-b^2)=(a+b)(a-b)$ , this becomes)

= $(sin^2theta-cos^2theta)(sin^2theta+cos^2theta)$

= $(sin^2theta-cos^2theta)*1$

= $-(cos^2theta-sin^2theta)$
(as $cos^2A-sin^2A=cos2A)$

= $-cos2theta$

How do you simplify the expression sin^4theta-cos^4thetasin^4theta-cos^4theta?